An Estimate Of The Essential Norm Of A Composition Operator Between Bloch-type Spaces In The Unit Ball

The title of this article is the estimate of the essential norm of a compositionoperator between Bloch-type spaces in the unit ball of C^n. That is to say, making useof the tool of the essential norm ,we get the upper estimate and the lower estimate ofthe composition operator which we have studied .In addition, we get a sufficient andnecessary condition for the composition operator to be compact. The article is dividedinto four parts.In the first part, some results and methods about operator theory in functionspaces of several complex variables, such as composition operators ,weightedcomposition operators and multipliers ,are introduced briefly .It can been seeing as apreface.In next part, some important concepts and theorems which are related to thearticle are given. Since they are well-known to everyone, the article only gives theresults but not prove them.The third part contains some lemmas and their proofs which are necessary to theproof of the main theorem.The last part gives the main theorem and its proof in the article, at the same timesome corollaries are obtained easily.